Tight-Binding Models in a Quasiperiodic Optical Lattice

This paper describes how one can use four standing wave laser fields to realize a two dimensional optical quasicrystal with eight-fold symmetry, closely related to the well-known octagonal or Ammann-Beenker tiling quasicrystal. We describe the structure and we outline the main features of an effective tight-binding model for atoms in this optical quasicrystal. Such a system, if realized experimentally, should provide valuable insights into the quantum properties of quasicrystals.